Which is More Acidic?

I think it would be 2-fluoro-4-nitrophenol because acidity is increased by the presence of electron withdrawing groups. 2-fluoro-4-nitrophenol has two electron withdrawing groups as opposed to only one for 4-nitrophenol. Is that correct? Should I also consider resonance when answering this question?

Sounds good to me. I would say that yes, you probably should consider resonance (the more resonance forms, the more stable the phenolate anion), just to show why the para nitro group draws electrons away from the ring. Also, since there's only one F, that shouldn't interfere with anything, it'll just inductively draw electron density from the ring.